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Scattering by complex fluids under shear
Scattering by complex fluids under shear Adrian R Rennie and Stuart M Clarke Scattering techniques are advancing knowledge of structural changes and phase behaviour in flowing systems; this information increases our understanding of rheological behaviour. Studies of sheared fluids at surfaces and experiments with synchrotron X-ray scattering on thin films are showinq' potential in the investigation of novel flow geometries. Experiments can now quantitatively test theoretical models and have, for example, highlighted the importance of hydrodynamic interparticle forces.
Address Polymers & Colloids Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK Current Opinion in Colloid & Interface Science 1996, 1:34-38
in the study of fluids under shear, most work has focused on elastic scattering, where there have been several interesting recent developments. Microscopy can provide real-space images of fluids under a range of conditions but interpretation of such data is often difficult and ambiguous. In many circumstances the spatial correlations between particles are more useful than their actual positions. Scattering techniques directly provide information on these correlations. In this review we will focus on in situ studies of flowing ~aterials rather than scattering experiments as a post-mortem diagnostic on quenched samples. Other established techniques, such as flow birefringence, have made a significant contribution to our understanding of the rheology of complex fluids and we refer the interested reader to a review of this work [1].
© Current Science Ltd ISSN 1359-0294
Advances in methods Introduction Complex fluids, such as those formed from particulate suspensions, micellar solutions and polymer melts, exhibit a wide range of non-Newtonian rheological behaviour; the viscosity and elastic response can vary with deformation rate and the history of the sample. Structural information, such as that available from scattering experiments, often provides a: better idea of the reasons for this complex behaviour than can measurements of rheological properties alone. Flow of complex fluids is enormously important in a whole range of industrial situations, regarding both transport of material and the structure that flow may impart to a product. Investigations of the transient structures form~d during the deformation of materials have therefore attracted considerable interest. This article will first provide an outline of advances in the techniques that are used to perform scattering studies of the structure of complex fluids under shear. Results of recent work on a variety of materials will then be described to illustrate the significant contributions that these studies are making to an understanding of rheological behaviour. In a typical scattering experiment, a beam of radiation such as light, X-rays or neutrons is directed on to a sample and is scattered away from the direction of the incident beam. In elastic scattering the energy of the radiation is unchanged and the angular or wavelength dependence of the scattered radiation provides information about the structure within the sample. Inelastic or quasi-elastic scattering involves some energy transfer- to or from the sample; these· energy changes can be related to the dynamic structure or motion within the sample. Although inelastic scattering and spectroscopic techniques, such as Raman scattering and NMR, are used
The geometry of a sheared system is illustrated in Figure 1 [2]. The three principle directions of the shear relative to the sample, flow, velocity gradient and vorticity directions are indicated in the figure relative to a two-dimensional detector. Until recently, the majority of work has used the Couette shear geometry of a cup rotating around a static inner cylinder. This configuration has the advantage of providing a well defined uniform shear but does not always provide easy access to data concerning the structure in all directions. A significant feature of recent work has been the interest in other flow environments or other geometries of the beam and sample. In part this interest has arisen from the finer collimation available to researchers using light [3-] and synchrotron X-ray beams [2,4--] than to those doing previous work with neutrons. Developments of these methods are providing new data with plate-plate, cone-plate and pipe flow geometries. Effects of oscillatory shear have attracted attention [2,5,6] as the time resolution of experiments is enhanced. A novel geometry has been developed to permit neutron reflection and low angle scattering studies of the interface of flowing dispersions at a solid surface [7--]. Experiments with a 20 mM dispersion of the cationic surfactant hexadecyl trimethylammonium 3,5 dichlorobenzoate in 020 have indicated hexagonal ordering of the worm-like micelles in the vorticity-gradient plane. The small angle scattering data are illustrated in Figure 2. Investigations using neutrons or light have been numerous and cover a variety of systems. In contrast, X-rays have been used for the. study of only a restricted number of systems under shear, such as a biaxial lamellar phase
Scattering by complex fluids under shear Rennie and Clarke
Figure 1
35
Figure 2
(a)
Gradient
t
~ Vorticity
~Flow
(b)
Small angle neutron-scattering data from a 20 mM solution of cetyltrimethylammonium 3,5 dichlorobenzoate in D:P against a quartz surface. The data has been reduced to allow for instrumental parameters and represents the change in differential cross'section for flow on versus flow off. Contours are factors of 2 on smoothed data. Reproduced with permission from [7··).
the sample depends upon the competing effects of shear, confinement and proximity of surfaces and could be investigated in all three flow directions with this apparatus.
Gradient
t
"",Vorticity
~Flow
The experimental geometry of a sheared system indicating the three principal directions. The incident beam is scattered by the sample onto the detector. The scattering (8) and the aximuthal ($) angles are shown. (a) Shows the beam incident along the vorticity axis. The scattering in this geometry is predominantly from structure in the flow-gradient plane. In (b) the beam is incident in the shear gradient direction, illustrating that the scattering is predominantly from structure in the vorticity-gradient plane. Adapted from (2) with permission.
formed from oolvstvrene-block-poly(ethylene-alt-propyd the lamellar phases of The latter study used a ratus where the diffraction constrained between two lined as the cylinders were fhe structure adopted by
Many materials, particularly concentrated dispersions, scatter light strongly and are opaque; however, it is sometimes still possible to use light-scattering techniques to investigate their behaviour. These methods include two-colour photon-correlation techniques in which crosscorrelation is used to ensure that only single particle motion is measured [8-]. This relatively new technique for studying motion within concentrated materials has not yet been applied to flowing systems. Alternatively, the scattering can be reduced by varying the refractive index of the dispersion medium to almost match that of the suspended particles. Such fluids can be transparent even at high concentrations, although the chemical nature of the system may have been significantly altered. This method has been applied to study the structures formed under flow by spherical colloidal particles [5,9]. Appropriate choice of solvents can be used to match the density as well as the refractive index in order to prevent the ordering that arises from sedimentation [3-]. Qualitative comparison of scattering data with patterns calculated from structural models or from the results of computer simulations have often been used to interpret results. Recently quantitative analysis of scattering data has been attempted, but is not always used. The advent of the charged coupled device as a two-dimensional light detector makes this quantitative analysis relatively easy ([3-], SM Clarke, JR Melrose, Ar Rennie, PJ Mitchel, Dt\l Heyes, unpublished data). Similar analysis can, of course, be made with neutron scattering data [10,11]. These quantitative analyses can provide detailed information, such as peak positions, shape and intensity, for comparison with theory, and provide more stringent tests of computer simulation models.
36
SCattering and surface forces
Contribution of scattering experiments to understanding of rheology The scattering patterns from charged, stabilized colloidal particles 'at rest can show long-range order, even large crystalline domains, under the appropriate conditions of low electrolyte concentrations. A continuing theme in the study of particulate dispersions has been the melting behaviour of such crystals under flow and the relation of the structural changes to rheological behaviour. On increasing the applied stress, the structural changes observed consist of the formation of a polycrystalline phase, subsequent formation of a sliding layer structure and finally complete disappearance of long-range order and the onset of shear thickening [12,13]. 'Banding' across a Couette cell, parallel to the flow direction, has been observed in these systems by direct optical observation, as illustrated in Figure 3. These bands consist of a disordered phase that co-exists with a more ordered one; the amount of the disordered phase increases with flow rate [14°]. Liquid-like dispersions of sterically stabilized polymer latex in organic media have been investigated and the results quantitatively compared with Brownian dynamics computer simulations (SM Clarke, JR Melrose AR Rennie, PJ Mitchell, OM Heyes, unpublished data) of hard spheres. This work, illustrated in Figure 4, suggests that models that do not include interparticle hydrodynamic interactions have limited applicability to concentrated dispersions. They also indicate technical requirements for simulations, in terms of the sizes and duration needed to obtain data of a precision adequate to observe the measured structural changes. Computer models without the hydrodynamic interactions tend to display a high degree of ordering, such as string phases which are not observed in experiments at equivalent moderate shear
rates. The subtle structural changes in these materials, which are reflected in the scattering patterns, can be readily observed with modern colour graphics available on computer screens and on the printed page. Other recent developments in particulate dispersions include an investigation by small angle neutron scattering of the gelation of silica particles and of how the morphology is affected by shear [15]. A further topic is the alignment of anisotropic particles, such as clays, under flow where diffraction techniques (SM clarke, P convert, AR Rennie, unpublished data), which avoid the complications of interparticle and particle form scattering, can directly give the orientation distribution of crystalline particles. Electro-rheological fluids have continued to be investigated [16]. The physiologically important system of red blood cells has been investigated in some detail over a number of years and continues to provide a range of interesting data [17,18], including measurements of deformability of particles as a function of shear. Theoretical analysis of scattering data from red blood cells has been developed to refine models for their orientational distribution and to allow for multiple scattering from concentrated dispersions [18]. Researchers have continued to study the alignment of a number of surfactant micelles [19°]. Systems include worm-like micelles [19°,20] and the nematic phases of discotic micelles [21]. The structural changes in both these systems, such as reorientation, can be associated with the different rheological regions. Lamellar and hexagonal liquid crystalline phases of surfactants have also been investigated under shear. Sometimes flow is used as a tool to align a mesophase, as
Figure 3
Photograph of a sample of colloidal silica spheres with a radius of 200 nm, with a 179 nm fluorescent core, at an estimated volume fraction of 0.28 in 0.0002 M Liel taken with a polarizing microscope under static (a) and sheared (b) conditions (average shear rate, approximately 0.22-0.29 s·I). Note the banding of the flowing material. Reproduced with permission from [14'].
Scattering by complex fluids under shear Rennie and Clarke
37
concentrated solutions of hexadecylpyridinium salts which can include added organic liquids and electrolyte. Isotropic to nematic transitions have been reponed to be induced by shear [23].
Figure 4
(a)
,=
o.
.0
6 10
Studies have also been made on a variety of other complex fluids such as polymer melts and mixtures of small molecules. We can only briefly highlight some examples that may be relevant to colloidal materials. In mixtures of small molecules, sudden cessation of shear is found to be equivalent, in terms of structural evolution, to a thermal quench producing phase separation [24]. Late-stage thermally induced spinodal decomposition of polymer blends under shear has been investigated, revealing elongation of the interdomain distance in the direction of flow [22]. The movement of the spinodal peak exhibits different power law exponents in the flow and vorticity directions, which are in turn different from static spinodal decomposition.
2.
(b)
Inten ity ( rbltary unl
Dhont [25] has indicated that the spinodal decomposition cannot be located by light scattering in a sheared system. Before phase separation in the homogeneous state, the turbidity becomes infinite for the first time on lowering the temperature far into the unstable region. What is measured, therefore, is the cloud point, which has a different location to the spinodal point in .the sheared system.
15.0
7.5
0.0 3.0
6.5
Q I mic:rom etr
10.0 -I
A 1.55 mm diameter polymethylmethacrylate latex bead sterically stabilized with poly(hydroxystearic acid) in bromocyloheptane at 400/0 w/w. Scattering patterns from the sample at rest and under (a) steady shear of Pedet number 70.0 in a plate-plate cell. Pedet number is defined here as (6ltTJ"I a3 ) 1"1 KT; where Tl is the medium viscosity. a is the particle diameter and y is the shear rate (b) Sections through the scattering pattern under shear in the flow (.) and vorticity. directions. The solid lines are fits to the data for the Ashcroft and Lekner model. Reproduced with permission from [3°].
it provides oriented or monodomain samples for structural studies [11]. Other experiments have been aimed at an understanding of rheological behaviour [22]. There are indications that micelles can grow under shear and that pre-existing micelles are not simply aligned [20]. A significant amount of work concerns the various aspects of phase transitions combined with the effects of shear. For example, several papers [11,20,23] have considered
Phase boundaries of polymer blends have been found to shift under shear; an example would be the homogenization of blends that occurs below their cloud point with increasing shear [26]. The phase-separated 'domains that are oriented by the flow give rise to textured structures which have been used to explain rheological behaviour [27]. Such morphology, however, can arise from fluid dynamic instabilities and data from scattering 'patterns should be combined with other observations on the sample to ensure the correct interpretation [28]. Block copolymers show a rich phase behaviour which can be perturbed by shear; particularly interesting arc crystal-ecrysral transitions [29] which may have analogues in the flow of particulate colloidal dispersions.
Outlook and conclusions We expect progress in the application of two-colour photon-correlation spectroscopy to sheared systems as mentioned earlier. The significant influence of surfaces on rheology and on the structure of complex fluids under shear has been recognized and should be the subject of further investigation [30·,31]. We expect extension of work beyond spherical particles to continue. For example, diffraction techniques are being developed to measure directly the alignment of anisotropic. crystalline particles which can be applied to. complex flow geometries (SM Clarke, P Convert, AR Rennire, unpublished data), which will complement more established techniques.
38
Scattering and surface forces
Acknowledgements
13.
Wc gratefully acknowledge the support of EI' SRC and ECC Intern ational and the Department of Trade and Indu stry Colloid Technology programme durin g the preparation of this review,
14.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: • ••
Wayland H: Streaming birefringence as a rheological research tool.) Polym Sci 1964 ,5:11-36.
2.
Okamoto S, Saijo K, Hashimoto T: Real·time SAXS observations of lamellar-forming block copolymers under large oscillatory shear deformation. Macromolecules 1994, 27:5547-5555.
Clarke SM, Ottewill RH, Rennie AR: light scattering studies of dispersions under shear. Adv Collo id Interface Sci 1995, 60:95-118. A light-scattering study from colloidal particles under shear in a medium that is density matched to the particles, presenting quantitative comparison of the results with those from liquid state models. The results of the model fitting can be interpreted as a change in effective volume fraction in the flow direction with increasing shear and can be related to the rheological behaviour of shear thinning by the Krieger-Dou gherty equation. 3. •
4.
Idziak SHJ, Safinya CR, Sirota EB, Bruinsma RF,Liang KS, Israelachvili IN: Structure of complex flu ids under flow and confinement, X-ray couette shear cell and the X-ray surface forces apparatus. ACS Symposium Series 1994, 578 :288-299. This paper describes a novel apparatus for the study with X-rays of liquid crystal phases under shear and under the influences of confinement and the proximity of surfaces.This paper appearsin an ACS Symposium volume with a number of other papers on structure in sheared systems. 5.
6.
Imhof A, Van Blaaderen A, Dhont JKG: Shear melting of colloIdal crystals of charged spheres studied with rheology and polarising microscopy. Langmuir 1994, 10:3477-3482. Although not describing scattering measurements, the direct optical observations made in this work are helpful in understanding the different length scales and ranges of order in sheared dispersions. 15.
Muzny CD, Straty GC, Hanley HJM: Small-angle neutron scattering study of dense sheared silica gels. Phys Rev 1994 , E50:R675-R678.
16.
Martin JE, Odinek J, Halsey TC: Structure of an electrorheological fluid In steady shear. Phys Rev 1994, E50:3263-3266.
17.
Gandjbakhche AH, Mills P, Snabre P: Light scattering technique for the study of orientation and deformation of red blood cells In a concentrated suspension. Applied Optics 1994, 33:1070-1078.
18.
Streekstra GJ, Hoekstra AG, Heethaar RM: Anomalous diffraction by arbitarily oriented ellipsoids: applications In ektacytometry. Applied Optics 1995, 33:7288-7296.
of special interest of outstanding interest
1.
Yan YO, Dhont JKG, Smits C, Lekkerkerker HNW: Oscillatoryshear-Induced order In nonaqueous dispersions of charged colloidal spheres. Physica 1994, A202 :68-80. Okamoto S, Saijo K, Hashimoto T: Dynamic SAXS studies of sphere forming block copolymers under large oscillatory shear deformation. Macromolecule s 1994, 27:3753-3758.
7.
Hamilton WA, Butler PO, Baker SM, Smith GS, Hayter JB, Magid U, Pynn R: Shear Induced hexagonal ordering In an IonIc viscoelastic fluid In flow past a surface. Phys Rev Letts 1994, 72:2219-2222. This work presents a novel technique for investigation of the solid-liquid interface. The results indicate ordering of thread like micelles in the vorticitygradient plane.
19.
Penfold J, Staples E, Kahn Lhodi A, Tucker I: The study of anlsotroplcally shaped micelles subjected to shear flow by small -angle neutron scattering. Int J Thermophysics 1995, 16:1109-1117. A useful review summarizing some neutron·scattering results on micelles under shear. This paper is from a volume 01 conference proceedings which contains a number of papers on scattering from sheared systems. 20.
Schmitt V, Schosseler F, Lequeux F: Structure of salt -free wormlike micelles: signature by SANS at rest and under shear. Europhys Letts 1995, 30 :31-36.
21.
Mang JT, Kumar S, Hammouda B: Discotic micellar nematic and lamellar phases under shear flow. Europhys Lells 1994, 28:489-494.
22.
lliuger J, Gronski W: A melt rheometer with Integrated small angle light scattering. Rheol Acta 1995, 34:70-79.
23.
Berret J-F, Roux DC, Porte G, Lindner P: Shear- Induced Isotroplc-to-nematic phase trans ition In equilibrium polymers. Europhys Letts 1994, 25:521-526.
24.
Beysens 0, Perrot F, Baumberger T: Phase separation In liquids due to quench by cessation of shear. Physica 1994, A204:76-86.
25.
Dhont JKG: Effects of shear flow on long-ranged correlations, spinodal demlxlng kinetics, and the location of the critical point and cloud point Int J Thermophysics 1994, 15:1157-1168.
26.
Wu R, Shaw MT, Weiss RA: A rheo-light-scattering instrument for the study of the phase behaviour of polymer blends under simple-shear flow. Rev Sci Instrum 1995, 66:2914-2921.
27.
Walker L, Wagner N: Rheology of region I flow in a Iylropic liquid-crystal polymer: the effects of defect texture. ) Rheol 1994,38:1525-1547.
28.
FerandezML, Higgins JS, Richardson SM: Flow Instabili ties In polymer blends under shear. Polymer 1995, 36:931-939.
29.
Jackson CL, Barnes KA, Morrison FA, Mays JW, Nakatani AI, Han CC: A shear-Induced Martensitic-Iike transformation In a block copolymer melt Macromolecules 1995, 28:713-722.
••
8.
Segre PN, van Megen W, Pusey PN, Schatzel K, Peters W: 2-Colour dynamic light scattering . ) Modern Optics 1995, 42:1929-1952. The technique of two-colour photon spectroscopy is described and its application to multiply'scattering colloidal suspensions is outlined. This technique should provide useful information on dynamicsof particles under shear when it is applied to flowing systems. 9.
Uu J, Weitz DA, Ackerson BJ: Coherent crystallography of shear aligned crystals of hard sphere colloids. Phys Rev 1993, E48:1106-1114.
10.
Diat 0, Raux 0, Nallet F: Lamellar phase under shear: SANS measurements. ) Physique IV 1993, C8,3:193-204.
11.
Raux DC, Berret J-F, Porte G, Peuvrel-Disdier E, Lindner P: Shear-Induced orientations and textures of nematic wormlike micelles. Macromolecules 1995, 28:1681-1687.
12.
Chow MK, Zukoski CF: Nonequilibrlum behaviour of dense suspensions of uniform particles: volume fraction and size dependence of rheology and microstructure. J Rheo/1995, 39:33-59. -
Chen LB, Chow MK, Ackerson BJ, Zukoski CF: Rheological and microstructural transitions In colloidal crystals. Langmuir 1994, 10:2817-2829.
30.
Chow MK, Zukoski CF: Gap size and shear history dependencies In shear thickening of a suspension ordered at rest J Rheol 1995, 39:15-32. This work indicates that the rheology of charged stabilized colloidal suspensions can be affected by the rheometer gap size and by wall effects. 31.
Palberg T, Streichel K: Resonant stick -slip motion In a colloidal crystal Nature 1994, 367 :51-54.
Address Polymers & Colloids Group, Cavendish Laboratory, Madingley Road, Cambridge CB3 OHE, UK Current Opinion in Colloid & Interface Science 1996, 1:34-38
in the study of fluids under shear, most work has focused on elastic scattering, where there have been several interesting recent developments. Microscopy can provide real-space images of fluids under a range of conditions but interpretation of such data is often difficult and ambiguous. In many circumstances the spatial correlations between particles are more useful than their actual positions. Scattering techniques directly provide information on these correlations. In this review we will focus on in situ studies of flowing ~aterials rather than scattering experiments as a post-mortem diagnostic on quenched samples. Other established techniques, such as flow birefringence, have made a significant contribution to our understanding of the rheology of complex fluids and we refer the interested reader to a review of this work [1].
© Current Science Ltd ISSN 1359-0294
Advances in methods Introduction Complex fluids, such as those formed from particulate suspensions, micellar solutions and polymer melts, exhibit a wide range of non-Newtonian rheological behaviour; the viscosity and elastic response can vary with deformation rate and the history of the sample. Structural information, such as that available from scattering experiments, often provides a: better idea of the reasons for this complex behaviour than can measurements of rheological properties alone. Flow of complex fluids is enormously important in a whole range of industrial situations, regarding both transport of material and the structure that flow may impart to a product. Investigations of the transient structures form~d during the deformation of materials have therefore attracted considerable interest. This article will first provide an outline of advances in the techniques that are used to perform scattering studies of the structure of complex fluids under shear. Results of recent work on a variety of materials will then be described to illustrate the significant contributions that these studies are making to an understanding of rheological behaviour. In a typical scattering experiment, a beam of radiation such as light, X-rays or neutrons is directed on to a sample and is scattered away from the direction of the incident beam. In elastic scattering the energy of the radiation is unchanged and the angular or wavelength dependence of the scattered radiation provides information about the structure within the sample. Inelastic or quasi-elastic scattering involves some energy transfer- to or from the sample; these· energy changes can be related to the dynamic structure or motion within the sample. Although inelastic scattering and spectroscopic techniques, such as Raman scattering and NMR, are used
The geometry of a sheared system is illustrated in Figure 1 [2]. The three principle directions of the shear relative to the sample, flow, velocity gradient and vorticity directions are indicated in the figure relative to a two-dimensional detector. Until recently, the majority of work has used the Couette shear geometry of a cup rotating around a static inner cylinder. This configuration has the advantage of providing a well defined uniform shear but does not always provide easy access to data concerning the structure in all directions. A significant feature of recent work has been the interest in other flow environments or other geometries of the beam and sample. In part this interest has arisen from the finer collimation available to researchers using light [3-] and synchrotron X-ray beams [2,4--] than to those doing previous work with neutrons. Developments of these methods are providing new data with plate-plate, cone-plate and pipe flow geometries. Effects of oscillatory shear have attracted attention [2,5,6] as the time resolution of experiments is enhanced. A novel geometry has been developed to permit neutron reflection and low angle scattering studies of the interface of flowing dispersions at a solid surface [7--]. Experiments with a 20 mM dispersion of the cationic surfactant hexadecyl trimethylammonium 3,5 dichlorobenzoate in 020 have indicated hexagonal ordering of the worm-like micelles in the vorticity-gradient plane. The small angle scattering data are illustrated in Figure 2. Investigations using neutrons or light have been numerous and cover a variety of systems. In contrast, X-rays have been used for the. study of only a restricted number of systems under shear, such as a biaxial lamellar phase
Scattering by complex fluids under shear Rennie and Clarke
Figure 1
35
Figure 2
(a)
Gradient
t
~ Vorticity
~Flow
(b)
Small angle neutron-scattering data from a 20 mM solution of cetyltrimethylammonium 3,5 dichlorobenzoate in D:P against a quartz surface. The data has been reduced to allow for instrumental parameters and represents the change in differential cross'section for flow on versus flow off. Contours are factors of 2 on smoothed data. Reproduced with permission from [7··).
the sample depends upon the competing effects of shear, confinement and proximity of surfaces and could be investigated in all three flow directions with this apparatus.
Gradient
t
"",Vorticity
~Flow
The experimental geometry of a sheared system indicating the three principal directions. The incident beam is scattered by the sample onto the detector. The scattering (8) and the aximuthal ($) angles are shown. (a) Shows the beam incident along the vorticity axis. The scattering in this geometry is predominantly from structure in the flow-gradient plane. In (b) the beam is incident in the shear gradient direction, illustrating that the scattering is predominantly from structure in the vorticity-gradient plane. Adapted from (2) with permission.
formed from oolvstvrene-block-poly(ethylene-alt-propyd the lamellar phases of The latter study used a ratus where the diffraction constrained between two lined as the cylinders were fhe structure adopted by
Many materials, particularly concentrated dispersions, scatter light strongly and are opaque; however, it is sometimes still possible to use light-scattering techniques to investigate their behaviour. These methods include two-colour photon-correlation techniques in which crosscorrelation is used to ensure that only single particle motion is measured [8-]. This relatively new technique for studying motion within concentrated materials has not yet been applied to flowing systems. Alternatively, the scattering can be reduced by varying the refractive index of the dispersion medium to almost match that of the suspended particles. Such fluids can be transparent even at high concentrations, although the chemical nature of the system may have been significantly altered. This method has been applied to study the structures formed under flow by spherical colloidal particles [5,9]. Appropriate choice of solvents can be used to match the density as well as the refractive index in order to prevent the ordering that arises from sedimentation [3-]. Qualitative comparison of scattering data with patterns calculated from structural models or from the results of computer simulations have often been used to interpret results. Recently quantitative analysis of scattering data has been attempted, but is not always used. The advent of the charged coupled device as a two-dimensional light detector makes this quantitative analysis relatively easy ([3-], SM Clarke, JR Melrose, Ar Rennie, PJ Mitchel, Dt\l Heyes, unpublished data). Similar analysis can, of course, be made with neutron scattering data [10,11]. These quantitative analyses can provide detailed information, such as peak positions, shape and intensity, for comparison with theory, and provide more stringent tests of computer simulation models.
36
SCattering and surface forces
Contribution of scattering experiments to understanding of rheology The scattering patterns from charged, stabilized colloidal particles 'at rest can show long-range order, even large crystalline domains, under the appropriate conditions of low electrolyte concentrations. A continuing theme in the study of particulate dispersions has been the melting behaviour of such crystals under flow and the relation of the structural changes to rheological behaviour. On increasing the applied stress, the structural changes observed consist of the formation of a polycrystalline phase, subsequent formation of a sliding layer structure and finally complete disappearance of long-range order and the onset of shear thickening [12,13]. 'Banding' across a Couette cell, parallel to the flow direction, has been observed in these systems by direct optical observation, as illustrated in Figure 3. These bands consist of a disordered phase that co-exists with a more ordered one; the amount of the disordered phase increases with flow rate [14°]. Liquid-like dispersions of sterically stabilized polymer latex in organic media have been investigated and the results quantitatively compared with Brownian dynamics computer simulations (SM Clarke, JR Melrose AR Rennie, PJ Mitchell, OM Heyes, unpublished data) of hard spheres. This work, illustrated in Figure 4, suggests that models that do not include interparticle hydrodynamic interactions have limited applicability to concentrated dispersions. They also indicate technical requirements for simulations, in terms of the sizes and duration needed to obtain data of a precision adequate to observe the measured structural changes. Computer models without the hydrodynamic interactions tend to display a high degree of ordering, such as string phases which are not observed in experiments at equivalent moderate shear
rates. The subtle structural changes in these materials, which are reflected in the scattering patterns, can be readily observed with modern colour graphics available on computer screens and on the printed page. Other recent developments in particulate dispersions include an investigation by small angle neutron scattering of the gelation of silica particles and of how the morphology is affected by shear [15]. A further topic is the alignment of anisotropic particles, such as clays, under flow where diffraction techniques (SM clarke, P convert, AR Rennie, unpublished data), which avoid the complications of interparticle and particle form scattering, can directly give the orientation distribution of crystalline particles. Electro-rheological fluids have continued to be investigated [16]. The physiologically important system of red blood cells has been investigated in some detail over a number of years and continues to provide a range of interesting data [17,18], including measurements of deformability of particles as a function of shear. Theoretical analysis of scattering data from red blood cells has been developed to refine models for their orientational distribution and to allow for multiple scattering from concentrated dispersions [18]. Researchers have continued to study the alignment of a number of surfactant micelles [19°]. Systems include worm-like micelles [19°,20] and the nematic phases of discotic micelles [21]. The structural changes in both these systems, such as reorientation, can be associated with the different rheological regions. Lamellar and hexagonal liquid crystalline phases of surfactants have also been investigated under shear. Sometimes flow is used as a tool to align a mesophase, as
Figure 3
Photograph of a sample of colloidal silica spheres with a radius of 200 nm, with a 179 nm fluorescent core, at an estimated volume fraction of 0.28 in 0.0002 M Liel taken with a polarizing microscope under static (a) and sheared (b) conditions (average shear rate, approximately 0.22-0.29 s·I). Note the banding of the flowing material. Reproduced with permission from [14'].
Scattering by complex fluids under shear Rennie and Clarke
37
concentrated solutions of hexadecylpyridinium salts which can include added organic liquids and electrolyte. Isotropic to nematic transitions have been reponed to be induced by shear [23].
Figure 4
(a)
,=
o.
.0
6 10
Studies have also been made on a variety of other complex fluids such as polymer melts and mixtures of small molecules. We can only briefly highlight some examples that may be relevant to colloidal materials. In mixtures of small molecules, sudden cessation of shear is found to be equivalent, in terms of structural evolution, to a thermal quench producing phase separation [24]. Late-stage thermally induced spinodal decomposition of polymer blends under shear has been investigated, revealing elongation of the interdomain distance in the direction of flow [22]. The movement of the spinodal peak exhibits different power law exponents in the flow and vorticity directions, which are in turn different from static spinodal decomposition.
2.
(b)
Inten ity ( rbltary unl
Dhont [25] has indicated that the spinodal decomposition cannot be located by light scattering in a sheared system. Before phase separation in the homogeneous state, the turbidity becomes infinite for the first time on lowering the temperature far into the unstable region. What is measured, therefore, is the cloud point, which has a different location to the spinodal point in .the sheared system.
15.0
7.5
0.0 3.0
6.5
Q I mic:rom etr
10.0 -I
A 1.55 mm diameter polymethylmethacrylate latex bead sterically stabilized with poly(hydroxystearic acid) in bromocyloheptane at 400/0 w/w. Scattering patterns from the sample at rest and under (a) steady shear of Pedet number 70.0 in a plate-plate cell. Pedet number is defined here as (6ltTJ"I a3 ) 1"1 KT; where Tl is the medium viscosity. a is the particle diameter and y is the shear rate (b) Sections through the scattering pattern under shear in the flow (.) and vorticity. directions. The solid lines are fits to the data for the Ashcroft and Lekner model. Reproduced with permission from [3°].
it provides oriented or monodomain samples for structural studies [11]. Other experiments have been aimed at an understanding of rheological behaviour [22]. There are indications that micelles can grow under shear and that pre-existing micelles are not simply aligned [20]. A significant amount of work concerns the various aspects of phase transitions combined with the effects of shear. For example, several papers [11,20,23] have considered
Phase boundaries of polymer blends have been found to shift under shear; an example would be the homogenization of blends that occurs below their cloud point with increasing shear [26]. The phase-separated 'domains that are oriented by the flow give rise to textured structures which have been used to explain rheological behaviour [27]. Such morphology, however, can arise from fluid dynamic instabilities and data from scattering 'patterns should be combined with other observations on the sample to ensure the correct interpretation [28]. Block copolymers show a rich phase behaviour which can be perturbed by shear; particularly interesting arc crystal-ecrysral transitions [29] which may have analogues in the flow of particulate colloidal dispersions.
Outlook and conclusions We expect progress in the application of two-colour photon-correlation spectroscopy to sheared systems as mentioned earlier. The significant influence of surfaces on rheology and on the structure of complex fluids under shear has been recognized and should be the subject of further investigation [30·,31]. We expect extension of work beyond spherical particles to continue. For example, diffraction techniques are being developed to measure directly the alignment of anisotropic. crystalline particles which can be applied to. complex flow geometries (SM Clarke, P Convert, AR Rennire, unpublished data), which will complement more established techniques.
38
Scattering and surface forces
Acknowledgements
13.
Wc gratefully acknowledge the support of EI' SRC and ECC Intern ational and the Department of Trade and Indu stry Colloid Technology programme durin g the preparation of this review,
14.
References and recommended reading Papers of particular interest, published within the annual period of review, have been highlighted as: • ••
Wayland H: Streaming birefringence as a rheological research tool.) Polym Sci 1964 ,5:11-36.
2.
Okamoto S, Saijo K, Hashimoto T: Real·time SAXS observations of lamellar-forming block copolymers under large oscillatory shear deformation. Macromolecules 1994, 27:5547-5555.
Clarke SM, Ottewill RH, Rennie AR: light scattering studies of dispersions under shear. Adv Collo id Interface Sci 1995, 60:95-118. A light-scattering study from colloidal particles under shear in a medium that is density matched to the particles, presenting quantitative comparison of the results with those from liquid state models. The results of the model fitting can be interpreted as a change in effective volume fraction in the flow direction with increasing shear and can be related to the rheological behaviour of shear thinning by the Krieger-Dou gherty equation. 3. •
4.
Idziak SHJ, Safinya CR, Sirota EB, Bruinsma RF,Liang KS, Israelachvili IN: Structure of complex flu ids under flow and confinement, X-ray couette shear cell and the X-ray surface forces apparatus. ACS Symposium Series 1994, 578 :288-299. This paper describes a novel apparatus for the study with X-rays of liquid crystal phases under shear and under the influences of confinement and the proximity of surfaces.This paper appearsin an ACS Symposium volume with a number of other papers on structure in sheared systems. 5.
6.
Imhof A, Van Blaaderen A, Dhont JKG: Shear melting of colloIdal crystals of charged spheres studied with rheology and polarising microscopy. Langmuir 1994, 10:3477-3482. Although not describing scattering measurements, the direct optical observations made in this work are helpful in understanding the different length scales and ranges of order in sheared dispersions. 15.
Muzny CD, Straty GC, Hanley HJM: Small-angle neutron scattering study of dense sheared silica gels. Phys Rev 1994 , E50:R675-R678.
16.
Martin JE, Odinek J, Halsey TC: Structure of an electrorheological fluid In steady shear. Phys Rev 1994, E50:3263-3266.
17.
Gandjbakhche AH, Mills P, Snabre P: Light scattering technique for the study of orientation and deformation of red blood cells In a concentrated suspension. Applied Optics 1994, 33:1070-1078.
18.
Streekstra GJ, Hoekstra AG, Heethaar RM: Anomalous diffraction by arbitarily oriented ellipsoids: applications In ektacytometry. Applied Optics 1995, 33:7288-7296.
of special interest of outstanding interest
1.
Yan YO, Dhont JKG, Smits C, Lekkerkerker HNW: Oscillatoryshear-Induced order In nonaqueous dispersions of charged colloidal spheres. Physica 1994, A202 :68-80. Okamoto S, Saijo K, Hashimoto T: Dynamic SAXS studies of sphere forming block copolymers under large oscillatory shear deformation. Macromolecule s 1994, 27:3753-3758.
7.
Hamilton WA, Butler PO, Baker SM, Smith GS, Hayter JB, Magid U, Pynn R: Shear Induced hexagonal ordering In an IonIc viscoelastic fluid In flow past a surface. Phys Rev Letts 1994, 72:2219-2222. This work presents a novel technique for investigation of the solid-liquid interface. The results indicate ordering of thread like micelles in the vorticitygradient plane.
19.
Penfold J, Staples E, Kahn Lhodi A, Tucker I: The study of anlsotroplcally shaped micelles subjected to shear flow by small -angle neutron scattering. Int J Thermophysics 1995, 16:1109-1117. A useful review summarizing some neutron·scattering results on micelles under shear. This paper is from a volume 01 conference proceedings which contains a number of papers on scattering from sheared systems. 20.
Schmitt V, Schosseler F, Lequeux F: Structure of salt -free wormlike micelles: signature by SANS at rest and under shear. Europhys Letts 1995, 30 :31-36.
21.
Mang JT, Kumar S, Hammouda B: Discotic micellar nematic and lamellar phases under shear flow. Europhys Lells 1994, 28:489-494.
22.
lliuger J, Gronski W: A melt rheometer with Integrated small angle light scattering. Rheol Acta 1995, 34:70-79.
23.
Berret J-F, Roux DC, Porte G, Lindner P: Shear- Induced Isotroplc-to-nematic phase trans ition In equilibrium polymers. Europhys Letts 1994, 25:521-526.
24.
Beysens 0, Perrot F, Baumberger T: Phase separation In liquids due to quench by cessation of shear. Physica 1994, A204:76-86.
25.
Dhont JKG: Effects of shear flow on long-ranged correlations, spinodal demlxlng kinetics, and the location of the critical point and cloud point Int J Thermophysics 1994, 15:1157-1168.
26.
Wu R, Shaw MT, Weiss RA: A rheo-light-scattering instrument for the study of the phase behaviour of polymer blends under simple-shear flow. Rev Sci Instrum 1995, 66:2914-2921.
27.
Walker L, Wagner N: Rheology of region I flow in a Iylropic liquid-crystal polymer: the effects of defect texture. ) Rheol 1994,38:1525-1547.
28.
FerandezML, Higgins JS, Richardson SM: Flow Instabili ties In polymer blends under shear. Polymer 1995, 36:931-939.
29.
Jackson CL, Barnes KA, Morrison FA, Mays JW, Nakatani AI, Han CC: A shear-Induced Martensitic-Iike transformation In a block copolymer melt Macromolecules 1995, 28:713-722.
••
8.
Segre PN, van Megen W, Pusey PN, Schatzel K, Peters W: 2-Colour dynamic light scattering . ) Modern Optics 1995, 42:1929-1952. The technique of two-colour photon spectroscopy is described and its application to multiply'scattering colloidal suspensions is outlined. This technique should provide useful information on dynamicsof particles under shear when it is applied to flowing systems. 9.
Uu J, Weitz DA, Ackerson BJ: Coherent crystallography of shear aligned crystals of hard sphere colloids. Phys Rev 1993, E48:1106-1114.
10.
Diat 0, Raux 0, Nallet F: Lamellar phase under shear: SANS measurements. ) Physique IV 1993, C8,3:193-204.
11.
Raux DC, Berret J-F, Porte G, Peuvrel-Disdier E, Lindner P: Shear-Induced orientations and textures of nematic wormlike micelles. Macromolecules 1995, 28:1681-1687.
12.
Chow MK, Zukoski CF: Nonequilibrlum behaviour of dense suspensions of uniform particles: volume fraction and size dependence of rheology and microstructure. J Rheo/1995, 39:33-59. -
Chen LB, Chow MK, Ackerson BJ, Zukoski CF: Rheological and microstructural transitions In colloidal crystals. Langmuir 1994, 10:2817-2829.
30.
Chow MK, Zukoski CF: Gap size and shear history dependencies In shear thickening of a suspension ordered at rest J Rheol 1995, 39:15-32. This work indicates that the rheology of charged stabilized colloidal suspensions can be affected by the rheometer gap size and by wall effects. 31.
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